Binary Systems and Dendrites

The hodograph equationEquationhodograph for solid–liquid interface movement is applied to the problem of chemical microsegragation and solute trappingTrappingsolute in a binary alloy. A specific method based on the one-point Cauchy problemCauchy problem is developed to solve the hodograph equationEquationhodograph with the solute diffusion equation. The method is tested in comparison with rapid solidification of Si–0.1 at.% As alloy previously analysed experimentally and using phase field modelling. To answer the question about reaching the steady state regime for dendriteDendrite growth from undercooled media, a model based on the hodograph equationEquationhodograph is presented. Using these advancements, an abrupt dropAbrupt drop in dendritic growth is analysed for glassGlass forming metallic melts.